Numerical Heat Transfer Part B Fundamentals · 1995 · 61 citations · 11 references
EngineeringMechanical EngineeringPhysicsHeat TransferThermal AnalysisThermodynamicsData AssimilationFinite Difference MethodsHeat Transfer AnalysisHeat Transfer ModelingInverse Heat TransferKalman FilteringFinite Difference SchemesHeat Flux ReconstructionInverse Conduction ProblemInverse Heat ConductionInverse Heat Conduction ProblemsKalman SmootherOne-dimensional Heat ConductionOne-dimensional Heat Transfer
Abstract The time-dependent surface heat flux at one boundary of a one-dimensional system is reconstructed by using the Kalman smoothing technique, given the initial temperature distribution and the time-temperature history at an interior location. The study makes a parametric investigation and analyzes the behavior of two finite-difference schemes. The numerical results show the very good performance of the proposed technique, which provides a comprehensive way for using future temperature measurements. Although in this study attention is devoted to the one-dimensional linear problem, the algorithm can be generalized for the stochastic nonlinear multidimensional case.
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Maximum likelihood estimates of linear dynamic systems
Herbert E. Rauch, F. Tung, Charlotte Striebel · AIAA Journal · 1965 · 1.9K citations